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Illustrations of flow nets
3D6 Environmental Engineering II
Dr Gopal Madabhushi
Trench supported by sheet piles
Impermeable clay
Uniform sand
5m
6m
6m
6m
Trench supported by sheet piles
Impermeable clay
Uniform sand
5m
6m
6m
6m
Trench supported by sheet piles
Impermeable clay
5m
6m
6m
6m
h=6mNh=10Nf=2.5+2.5
Uniform sand
Excavation supported by a sheet pile
Shale
Uniform sand
Water pumped away
Steel sheet
Excavation supported by a sheet pile
Shale
Uniform sand
Water pumped away
Steel sheet
Reduced sheet penetration; possible liquefaction v = 0
Shale
Uniform sand
Steel sheet
Reduced sheet penetration; possible liquefaction v = 0
Uniform sand
Reservoir Tail water
Shale
Concrete dam or weir
Reservoir Tail water
Shale
Uniform sand
Concrete dam with cut-off; reduces uplift pressure
Reservoir
Shale
Uniform sand
Concrete dam with cut-off; reduces uplift pressure
Reservoir
Shale
Uniform sand
Pumped well in confined aquifer
Observation wellpumped wellElevationAquifer heads
H
D aquiferRadial flow
Impermeable stratum
Plan
Pumped well in confined aquifer
Observation wellpumped wellElevationAquifer heads
H
D aquiferRadial flow
Impermeable stratum
Plan
Clay dam, no air entry
Shale
clay
reservoiratmospheric line
drain
Clay dam, no air entry
Shale
clay
atmospheric line
drainreservoir
Clay dam, no air entry
Observation well
Shale
clay
atmospheric line
drainreservoir
Clay dam, no air entry, reduced drain; seepage out of downstream face
Shale
clay
atmospheric lineNot possible
reservoir
Clay dam, with air entry
Shale
clay
reservoir
drain
Clay dam, with air entry
Shale
clay
reservoir
drain
Clay dam, no capillary, reduced drain; seepage out of downstream face
Shale
clay
reservoir
Clay dam, no capillary, reduced drain; seepage out of downstream face
Shale
clay
reservoir
Flow of water in earth dams
The drain in a rolled clay dam will be made of gravel, which has an effectively infinite hydraulic conductivity compared to that of the clay, so far a finite quantity of flow in the drain and a finite area of drain the hydraulic gradient is effectively zero, i.e. the drain is an equipotential
The phreatic surface connects points at which the pressure head is zero. Above the phreatic surface the soil is in suction, so we can see how much capillarity is needed for the material to be saturated. If there is insufficient capillarity, we might discard the solution and try again. Alternatively: assume there is zero capillarity, the top water boundary is now atmospheric so along it and the flow net has to be adjusted within an unknown top boundary as the phreatic surface is a flow line if there is no capillarity.
Flow of water in earth dams
yh
If then in the flow net, so once we have the phreatic surface we can put on the starting points of the equipotentials on the phreatic surface directly
Flow of water in earth dams
yh consyh
Unsteady flow effects
Consolidation of matrixChange in pressure head within the soil due to
changes in the boundary water levels may cause soil to deform, especially in compressible clays. The soil may undergo consolidation, a process in which the voids ratio changes over time at a rate determined by the pressure variation and the hydraulic conductivity, which may in turn depend on the voids ratio.
Liquefaction (tensile failure)The total stress normal to a plane in the soil can be separated
into two components, the pore pressure p and the effective inter-granular stress ’:
By convention in soils compressive stresses are +ve.Tensile failure occurs when the effective stress is less than the
fracture strength ’fracture, and by definition for soil ’fracture=0. When the effective stress falls to zero the soil particles are no longer in contact with each other and the soil acts like a heavy liquid. This phenomenon is called liquefaction, and is responsible to quick sands.
Breakdown of rigid matrix
p
Uniform soil of unitweight
Upward flow of water
Large upward hydraulic gradients:
Uniform soil of unitweight
Upward flow of water
Plug of Base areaA
Water table and datum
standpipe
Gap opening as plug rises
Critical head Pressure hcrit
Critical potentialHead zhh critcrit
z
At the base of the rising plug, if there is no side friction:
wcrit
v
hp
z
.
.
So if v=0 then v = p and :
wcritwcrit zhhz ...
w
wcritcrit z
hi
, icrit=0.8~1.0
where icrit is the critical hydraulic gradient for the quick sandCondition. As 18~20 kN/m3 for many soils (especially sandsand silts) and w 10 kN/m3 :
0.110
1020
z
hi critcrit
Frictional (shear failure)
Sliding failure of a gravity concrete dam due to insufficient friction along the base:
Uniform sand
Reservoir Tail waterWH1H2
W´ dspU .
Limiting condition on shear force T is:
maxmax tan. WT
where tan’max is the co-efficient of friction, so considering the base of the dam we are looking for:
21max HHF
where W‘ = W-U is the effective weight of the dam, U is thetotal uplift due to the pore pressure distribution p along the baseof the dam, and F = H1- H2 is the shear force along the Dam base
